Fuzzy Sets and Systems 136 (2003) 115–119 www.elsevier.com/locate/fss Representation of fuzzy subalgebras by crisp subalgebras U.M. Swamy a ; ∗ , N.V.E.S. Murthy b a Department of Mathematics, Andhra University, Visakhapatnam - 530 003, India b A.U.P.G. Centre, Etcherla, Srikakulam - 532 402, India Received 28 June 1995; received in revised form 6 June 2002; accepted 14 June 2002 Abstract For any universal algebra, another universal algebra of the same type is constructed in such a way that there is a one-to-one correspondence between the fuzzy subalgebras of the former and certain crisp subalgebras of the latter. c  2002 Elsevier Science B.V. All rights reserved. MSC: primary 03E72; secondary 08A05; 08A30 1. Introduction Ever since Zadeh [6] introduced the notion of the fuzzy subset of a set, several mathematicians introduced and studied fuzzy substructures of many algebraic structures. However, Swamy and Raju [3,4] and Weinbeger [5] have unied all these fuzzy algebraic notions, by introducing the concept of fuzzy algebraic systems and making a detailed study of the same. In this paper we establish that the notions of fuzzy algebraic substructures are very close to the corresponding crisp algebraic structures, by proving that, for any universal algebra of a given type, there exists a universal algebra of the same type such that the fuzzy subalgebras of the former are in one-to-one correspondence with certain crisp subalgebras of the later. This shows that the study of fuzzy subalgebras is subsumed in that of crisp subalgebras. * Corresponding author. E-mail address: drnvesmurthy@redimail.com.in (U.M. Swamy). 0165-0114/03/$ - see front matter c  2002 Elsevier Science B.V. All rights reserved. PII:S0165-0114(02)00342-1